# 3-D PTV measurement of Marangoni convection in liquid bridge in space experiment

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- Received:
- Revised:
- Accepted:

DOI: 10.1007/s00348-011-1136-9

- Cite this article as:
- Yano, T., Nishino, K., Kawamura, H. et al. Exp Fluids (2012) 53: 9. doi:10.1007/s00348-011-1136-9

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## Abstract

Microgravity experiments have been conducted on the International Space Station in order to clarify the transition processes of the Marangoni convection in liquid bridges of high Prandtl number fluid. The use of microgravity allows us to generate large liquid bridges, 30 mm in diameter and up to 60 mm in length. Three-dimensional particle tracking velocimetry (3-D PTV) is used to reveal complex flow patterns that appear after the transition of the flow field to oscillatory states. It is found that a standing-wave oscillation having an azimuthal mode number equal to one appears in the long liquid bridges. For the liquid bridge 45 mm in length, the oscillation of the flow field is observed in a meridional plane of the liquid bridge, and the flow field exhibits the presence of multiple vortical structures traveling from the heated disk toward the cooled disk. Such flow behaviors are shown to be associated with the propagation of surface temperature fluctuations visualized with an IR camera. These results indicate that the oscillation of the flow and temperature field is due to the propagation of the hydrothermal waves. Their characteristics are discussed in comparison with some previous results with long liquid bridges. It is shown that the axial wavelength of the hydrothermal wave observed presently is comparable to the length of the liquid bridge and that this result disagrees with the previous linear stability analysis for an infinitely long liquid bridge.

### List of symbols

*Ar*Aspect ratio [−]

*D*Disk diameter [m]

*f*Frequency [Hz]

*H*Length of the liquid bridge [m]

*m*Azimuthal mode number [−]

*Ma*Marangoni number [−]

*Ma*_{c}Critical Marangoni number [−]

*Pr*Prandtl number [−]

*r*Radial position [m]

*t*Time [s]

*T*Oscillation period [s] or temperature [K]

*T*_{c},*T*_{h}Cooled-disk temperature and heated-disk temperature [K]

- Δ
*T* Temperature difference [K]

- Δ
*T*_{c} Critical temperature difference [K]

*V*Liquid bridge volume [m

^{3}]*V*_{0}Gap volume [m

^{3}]*Vr*Volume ratio (=

*V*/*V*_{0}) [−]*z*Axial position [m]

### Greek symbols

*α*Thermal diffusivity [m

^{2}/s]*λ*_{z}Axial wavelength [m]

*ν*Kinematic viscosity [m

^{2}/s]*ρ*Density [kg/m

^{3}]*σ*Surface tension [N/m]

*σ*_{T}Temperature coefficient of surface tension [N/(m·K)]